The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility model

TY - JOUR

T1 - The eigenvalues of the sample covariance matrix of a multivariate heavy-tailed stochastic volatility model

AU - Janßen, Anja

AU - Mikosch, Thomas Valentin

AU - Rezapour Toughari, Mohsen

AU - Xie, Xiaolei

PY - 2018/5

Y1 - 2018/5

N2 - We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for the ordered eigenvalues and corresponding eigenvectors. Essentially, we consider two different cases where the tail behavior either stems from the i.i.d. innovations of the process or from its volatility sequence. In both cases, we make use of a large deviations technique for regularly varying time series to derive multivariate α-stable limit distributions of the sample covariance matrix. For the case of heavy-tailed innovations, we show that the limiting behavior resembles that of completely independent observations. In contrast to this, for a heavy-tailed volatility sequence the possible limiting behavior is more diverse and allows for dependencies in the limiting distributions which are determined by the structure of the underlying volatility sequence.

AB - We consider a multivariate heavy-tailed stochastic volatility model and analyze the large-sample behavior of its sample covariance matrix. We study the limiting behavior of its entries in the infinite-variance case and derive results for the ordered eigenvalues and corresponding eigenvectors. Essentially, we consider two different cases where the tail behavior either stems from the i.i.d. innovations of the process or from its volatility sequence. In both cases, we make use of a large deviations technique for regularly varying time series to derive multivariate α-stable limit distributions of the sample covariance matrix. For the case of heavy-tailed innovations, we show that the limiting behavior resembles that of completely independent observations. In contrast to this, for a heavy-tailed volatility sequence the possible limiting behavior is more diverse and allows for dependencies in the limiting distributions which are determined by the structure of the underlying volatility sequence.

U2 - 10.3150/16-bej901

DO - 10.3150/16-bej901

M3 - Journal article

SN - 1350-7265

VL - 24

SP - 1351

EP - 1393

JO - Bernoulli

JF - Bernoulli

IS - 2

ER -